Multiplying Monomials (Values and Variables) over Unit Fraction (Level 3)

This topic covers the skills of multiplying monomials, which include both values and variables, within the context of working with radicals and unit fractions. It is designed to strengthen understanding of radical expressions, specifically how to multiply and simplify them when placed over a unit fraction. Each question presents a different set of variables and powers, requiring the application of rules for multiplying radicals and simplifying the resulting expressions. This is a more advanced practice in dealing with radicals, aimed at students ready for higher-level algebraic operations.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Radicals - Multiplying Monomials (Values and Variables) over Unit Fraction Worksheet

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Math worksheet on 'Radicals - Multiplying Monomials (Values and Variables) over Unit Fraction (Level 3)'. Part of a broader unit on 'Radicals - Multiplication Intro' Learn online: app.mobius.academy/math/units/radicals_multiplication_intro/
1
A LaTex expression showing \frac{square root of 12r{n to the power of 3 } times square root of 175{r to the power of 4 {n} to the power of 2 }}{1 over 2 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 40{r} to the power of 2 {n} to the power of 3 square root of 21r
b A LaTex expression showing 10{r} to the power of 2 {n} to the power of 3 square root of 21rn
c A LaTex expression showing 10{r} to the power of 2 {n} to the power of 2 square root of rn
d A LaTex expression showing 20{r} to the power of 2 {n} to the power of 2 square root of 21rn
e A LaTex expression showing 10{r} to the power of 3 {n} to the power of 2 square root of 21rn
2
A LaTex expression showing \frac{square root of 175{r to the power of 2 {p} to the power of 4 } times square root of 18{p to the power of 3 }}{1 over 3 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 15{r} to the power of 2 {p} to the power of 3 square root of 14p
b A LaTex expression showing 45r{p} to the power of 3 square root of 14p
c A LaTex expression showing 15r{p} to the power of 3 square root of 14p
d A LaTex expression showing 15r{p} to the power of 3 square root of 14
3
A LaTex expression showing \frac{square root of 52y{z to the power of 4 } times square root of 20{y to the power of 3 {z} to the power of 4 }}{1 over 4 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 16{y} to the power of 2 {z} to the power of 4 square root of 65
b A LaTex expression showing 64{y} to the power of 2 {z} to the power of 4
c A LaTex expression showing 4{y} to the power of 3 {z} to the power of 4 square root of 65
d A LaTex expression showing {y} to the power of 2 {z} to the power of 4
e A LaTex expression showing 4{y} to the power of 2 {z} to the power of 4 square root of 65y
4
A LaTex expression showing \frac{square root of 99{c to the power of 4 } times square root of 48n}{1 over 4 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 12csquare root of 33cn
b A LaTex expression showing 192csquare root of 33cn
c A LaTex expression showing 48{c} to the power of 2 square root of 33n
d A LaTex expression showing 12{c} to the power of 2 square root of 33n
e A LaTex expression showing 12{c} to the power of 2 square root of 33
5
A LaTex expression showing \frac{square root of 20{m to the power of 3 {p} to the power of 2 } times square root of 44p}{1 over 3 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 4m{p} to the power of 2 square root of 55mp
b A LaTex expression showing 4mpsquare root of 55m
c A LaTex expression showing 36mpsquare root of 55mp
d A LaTex expression showing 4mpsquare root of 55mp
e A LaTex expression showing 12mpsquare root of 55mp
6
A LaTex expression showing \frac{square root of 75{p to the power of 2 {n} to the power of 2 } times square root of 20p{n to the power of 3 }}{1 over 2 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 20p{n} to the power of 2 square root of 15pn
b A LaTex expression showing 40{p} to the power of 2 {n} to the power of 2 square root of 15n
c A LaTex expression showing 10p{n} to the power of 2 square root of 15pn
d A LaTex expression showing 10{p} to the power of 2 {n} to the power of 2 square root of 15pn
e A LaTex expression showing p{n} to the power of 2 square root of pn
7
A LaTex expression showing \frac{square root of 27{p to the power of 2 {m} to the power of 4 } times square root of 32}{1 over 2 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 12p{m} to the power of 2
b A LaTex expression showing 12p{m} to the power of 2 square root of 6
c A LaTex expression showing 24p{m} to the power of 2 square root of 6
d A LaTex expression showing 48{m} to the power of 2 square root of 6
e A LaTex expression showing 60p{m} to the power of 2 square root of 6
Radicals - Multiplying Monomials (Values and Variables) over Unit Fraction (Level 3) - Mobius Math Academy